An arch pushes outward on its supports as well as down. For the same load and span the horizontal push grows as the rise falls: halve the rise and you roughly double the thrust.
H ≈ w·s² ⁄ 8f (uniform load w per metre, span s, rise f)
Rules · Cities · Plans · Proportion
The prince’s piazza at the centre
At the centre of the city lay out the main piazza as a rectangle twice as long as it is wide, with the cathedral at one end and the prince’s palace at the other, and put a merchants’ square and a market square beside it.
Sforzinda: main piazza 300 × 150 braccia (about 175 × 90 m)
Filarete’s architect lays out the centre of Sforzinda before anything else is built. The cathedral and the prince’s palace face each other down the length of the great piazza, so that the two powers of the city share one open space; the lesser squares at its sides take trade, the markets and the offices of city government. The whole centre is a composition of rectangles in simple ratios, the piazza itself a double square.
Filarete gives his dimensions in Milanese braccia (a braccio is about 0.6 m). In this model the centre is built at that size, while the city round it is much reduced from Filarete’s enormous circle, so the piazza looks larger in proportion than it would in Sforzinda.
Related rules
To find how thick the pier of an arch must be, divide the intrados into three equal parts; draw a line from the springing through the first division, and produce it beyond the springing by its own length. A vertical through the end of that line marks the outer face of the pier.
pier ≈ ¼ span (semicircle) · ≈ 0.23 span (equilateral) · less for a lancet
Give the villa garden porticoes for sun and for shade, grottoes made in imitation of nature with tufa and shells, evergreens planted in straight rows at equal distances, and hedges of box; set vines on columns over the walks.
Lay the ideal garden out on a circular plan in concentric rings, woods outside, then meadows and orchards, then gardens of knots and clipped evergreens divided by walks, with water and the fountain of the goddess at the centre.
A column is narrower at the top than at the bottom, but the taller the column the less it should be diminished, because distance already makes its top look smaller.
upper Ø : lower Ø = 5⁄6 (≤15 ft) · 11⁄13 (15–20 ft) · 6⁄7 (20–30 ft) · 13⁄15 (30–40 ft) · 7⁄8 (40–50 ft)
Columns may be spaced 1½ diameters apart (pycnostyle), 2 (systyle), 2¼ (eustyle), 3 (diastyle) or more (araeostyle). The eustyle, with a wider central bay of 3 diameters, is the best for use and beauty.
clear space = 1½ · 2 · 2¼ · 3 · >3 D
Cite this page Chris Paton, “The prince’s piazza at the centre”, The Textbook of Architecture, https://textbookofarchitecture.com/rule/filarete-central-piazza. Text, drawings and models licensed under CC BY-NC 4.0.